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What I found:

1. Select should be FALSE when comparing with AIC

2. Select=TRUE ONLY when we have a single model in mind (instead of comparing many models with AIC)

3. All models being compared should be fit with method=ML when unpenalized fixed effects (parametric terms) are present (like here)

4. Method=REML is fine though for comparing "nested" GAM(M) models in AIC when all effects are fully penalized

Found a great tutorial on GAMs from Gavin here which covers most of this.